In a previous work we described a new method to speed up the computation of a Language Model look-ahead in a speech recognizer with a tree organized lexicon. Three different mechanisms were employed to avoid a redundant computation of the probabilities: a node level cache memory, a pre-calculation of active contexts and a perfect hash LM organization. This strategy allowed us to apply a trigram based LM to compute the look-ahead with important computational savings in comparison with the usual bigram or unigram approximation. In this paper we describe several improvements to the pre-calculation of active contexts that allow us to achieve further time reductions.